Answer :
The end behavior of the function are [tex]\text{As } x \to -3^-, \text{f(x)} \to -\infty[/tex] and [tex]\text{As } x \to -3^+, \text{f(x)} \to \infty[/tex]
From the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
The reciprocal function
First, we can see that
As x approaches infinity, the function approaches -1
This is represented by the horizontal asymptote
So, we have
[tex]\text{As } x \to \infty, \text{f(x)} \to -1[/tex]
We also have that
The function has a vertical asymptote at x = -3
The behavior of the function around this value are
[tex]\text{As } x \to -3^+, \text{f(x)} \to \infty[/tex]
[tex]\text{As } x \to -3^-, \text{f(x)} \to -\infty[/tex]
These represent the end behavior of the function
